Time Limit: 1000MS | Memory Limit: 65536K | |
Total Submissions: 22621 | Accepted: 10157 |
Description
Bessie has gone to the mall‘s jewelry store and spies a charm bracelet. Of course, she‘d like to fill it with the best charms possible from the N (1 ≤ N ≤ 3,402) available charms. Each charm i in the supplied list has a weightWi (1 ≤ Wi ≤ 400), a ‘desirability‘ factor Di (1 ≤ Di ≤ 100), and can be used at most once. Bessie can only support a charm bracelet whose weight is no more than M (1 ≤ M ≤ 12,880).
Given that weight limit as a constraint and a list of the charms with their weights and desirability rating, deduce the maximum possible sum of ratings.
Input
* Line 1: Two space-separated integers: N and M
* Lines 2..N+1: Line i+1 describes charm i with two space-separated integers: Wi and Di
Output
* Line 1: A single integer that is the greatest sum of charm desirabilities that can be achieved given the weight constraints
Sample Input
4 6 1 4 2 6 3 12 2 7
Sample Output
23
题意:给定物品数量n和背包容量m,n个物品的重量weight和价值val,求能获得的最大价值。
题解:状态转移方程:dp[i][j] = max(dp[i-1][j], dp[i-1][j-w[i]] + v[i]);当中状态dp[i][j]表示前i个物品放在容量为j的背包中能获得的最大价值。二维数组能够压缩成一维以节省空间,可是内层循环须要倒序。
原始版本号:耗时360ms
#include <stdio.h> #define maxn 12882 int dp[maxn]; int max(int a, int b){ return a > b ? a : b; } int main() { int n, totalWeight, i, j, weight, val; scanf("%d%d", &n, &totalWeight); for(i = 1; i <= n; ++i){ scanf("%d%d", &weight, &val); for(j = totalWeight; j; --j){ if(j >= weight) dp[j] = max(dp[j], dp[j - weight] + val); } } printf("%d\n", dp[totalWeight]); return 0; }<span style="font-family:FangSong_GB2312;"> </span>
优化后的代码:耗时219ms
#include <stdio.h> #define maxn 12882 int dp[maxn]; int main() { int n, totalWeight, i, j, weight, val; scanf("%d%d", &n, &totalWeight); for(i = 1; i <= n; ++i){ scanf("%d%d", &weight, &val); for(j = totalWeight; j; --j){ if(j >= weight && dp[j - weight] + val > dp[j]) dp[j] = dp[j - weight] + val; } } printf("%d\n", dp[totalWeight]); return 0; }
用二维dp数组写了一个,果断的超了内存,占用内存大概12882*3404*4/1024=171兆。题目限制是65兆
TLE:
#include <stdio.h> #define maxn 12882 int dp[3404][maxn]; int max(int a, int b){ return a > b ? a : b; } int main() { int n, m, weight, val, i, j; scanf("%d%d", &n, &m); for(i = 1; i <= n; ++i){ scanf("%d%d", &weight, &val); for(j = 1; j <= m; ++j) if(j >= weight) dp[i][j] = max(dp[i-1][j], dp[i-1][j-weight] + val); else dp[i][j] = dp[i-1][j]; } printf("%d\n", dp[n][m]); return 0; }